{"paper":{"title":"Polynomial and exponential stability of $\\theta$-EM approximations to a class of stochastic differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chong Zhang, Guangqiang Lan, Yunjiao Hu","submitted_at":"2014-07-06T11:35:53Z","abstract_excerpt":"Both the mean square polynomial stability and exponential stability of $\\theta$ Euler-Maruyama approximation solutions of stochastic differential equations will be investigated for each $0\\le\\theta\\le 1$ by using an auxiliary function $F$ (see the following definition (2.3)). Sufficient conditions are obtained to ensure the polynomial and exponential stability of the numerical approximations. The results in Liu et al [12] will be improved and generalized to more general cases. Several examples and non stability results are presented to support our conclusions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1486","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}